A Toronto space is an uncountable non-discrete Hausdorff space which
is
homeomorphic to every one of it's uncountable subspaces. It is known
that a Toronto space, if one exixts, is scattered of Cantor-Bendixon
rankw1 with each level countable. J. Steprans defines an
a-Toronto space, where a is an ordinal, to be a scattered space of
rank a which is homeomorphic to each subspace of the same rank. We
will
discuss results related to our recent proof that, consistently, there
are countable a-Toronto spaces for any a < w1; for example, we
show that the proof can be modified to obtain, for any cardinal k, a
k-Toronto space in which each level has cardinality k.